You still have your usual pokeblocks, they work as before but you no longer have that machine with the other people, now you got an item called PokéBlock Kit which basicly allows you to instantly make pokeblocks out of a max of 4 berries, each block can increase the old Cool, Beautiful, Cute etc stats.
Besides that it stays around the same as the old gen 3 contest, contests are divided by each of the stats, Coolness contest, Beauty Contest etc.
They start with a Introduction Round. It stays the same as gen 3 since it will evaluate your pokemon by how much of that contest's stat the pokemon has (more Cool stat means more evaluation in the Coolness Contest). The only diference is that your pokemon can hold an item which will increase one of the stats even more, you can obtain this item (a scarf) by speaking to the Pokémon Fan Club boss and show him a pokemon with the max of a certain stat and he will give you the respective scarf (show him a pokemon with max beauty and you get a beauty scarf)
The next round is the Talent Round, basicly its also the same thing with the old exciting 5 star meter. The only thing new i think is the moves combo, you can read all the combos here:
https://www.serebii.net/omegarubyalphasapphire/contestcombos.shtml
Besides that its all the same, some minor new things is you are given a pikachu which cosplays like a certain stat increasing it (you can chance costume you go to a wardrobe in the contest hall) and the fact that you get items from fans like berries if you win